Metamaterials are materials engineered to have properties that do not occur naturally. Mechanical metamaterials are “designer” materials with exotic mechanical properties mainly controlled by their unique architecture rather than their chemical make-up. While a number of such mechanical metamaterials exist, one class of such mechanical metamaterials is known as auxetic materials (or simply “auxetics”). Auxetics are materials which have a negative Poisson's ratio. The Poisson's ratio (ν) of any material is the ratio between the transverse strain εt and the longitudinal strain εl in the loading direction (wherein ν=−εt/εl). Accordingly, for negative Poisson's ratio materials (i.e. ν is negative) auxetics become wider and/or thicker, rather than thinner, when stretched. In other words, such auxetics which have a negative Poisson's ratio become thicker and/or wider in a direction perpendicular to the direction of the applied force.
A variety of geometrically-generated auxetics are known. In many cases, for example, a planar sheet of material may be perforated with a given geometric pattern in order to produce a geometric configuration which will enable an auxetic response (i.e. the planar sheet will get transversely wider, rather than thinner) when the material is stretched in a longitudinal loading direction. The planar sheet may for example be perforated with incisions extending in predetermined directions and patterns, thereby forming the predetermined geometric configuration in the material which will enable the desired auxetic response when a tensile force is applied to the material in a predetermined loading direction. The resulting auxetic behavior can be tuned (either isotropically or anisotropically) at targeted expandability, a feature that can be an asset for highly flexible and stretchable devices.
While the unusual behaviour of auxetics, governed by their negative Poisson's ratio, has been found to be well-suited for designing shape transforming metamaterials, there exists challenges with current auxetic designs that use monolithic materials, including the fact that they are “monostable” (i.e. they cannot maintain the transformed shape upon load removal). Existing auxetics that are obtained from such elastic monolithic materials therefore resume to their un-deformed configuration upon load removal.
Shape transformations using such monostable auxetic materials can be programmed by exploiting the nontrivial deformation modes pertinent to elastic instabilities. However, achieving shape alterations that are robust and stable is challenging, since a pre-stressed state has to be maintained in the structure to maintain its deformed shape.